If you're thinking in terms of Facebook showing deleted updates to law enforcement to track down activists — or some rogue employee at Facebook HQ taking a peek — then we're talking about totally different levels of paranoia. Sure, that is a legitimate concern for the relative few who have something to fear from powerful governments.
For the rest of us, though, someone we unfriend (an ex-partner, for example) being able to archive and still access all of our old photos/updates is a much bigger concern. I argue that distributed social software should follow Facebook's lead and offer a sane default of not having such an archiving feature, and not going out of its way to make it particularly easy to add one, either. Otherwise the "creepy" aspect of not being able to rescind access to your photos/updates is going to be a serious downside to this new network, and could keep people from using it.
Edited to add:
Also, what's more secure in theory isn't always more secure in practice. Moxie Marlinspike observed that the original version of Cryptocat (which did end-to-end encryption in JS) was potentially less safe than Gchat. Why? Because if you compromised Cryptocat's server, you could make it serve JS with a hidden backdoor. And Cryptocat, being a one-man shop, would likely be a softer target than a company like Google, which has had plenty of time and expertise hardening their systems. How much do you trust the guy behind Cryptocat, versus Google with their reputation to protect?
Along the same lines, imagine you use a hosted Tent server for social networking — you don't have time to bother running your own server, but you've heard Tent keeps your data safe from Facebook, so it'll protect your privacy better, right? But then the random guy hosting your Tent account turns around and leaks your info. Or he's running old software with a vulnerability in it, and gets pwned. Suddenly hackers have all your data. Would that have happened on Facebook?
When I was curious about signing up with Diaspora, one of the open community pods had a cheeky note from the server admin saying basically that he would peek in and read your stuff if he felt like it. So this is not entirely hypothetical. I'm a huge fan of efforts like Tent, but let's not forget there are upsides to Facebook and Google's stewardship, and an alternative system can easily have as many privacy/security cons as it does pros. Tread carefully.